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基于最大平均差异的迁移模糊C均值聚类

焦连猛 王丰 潘泉

焦连猛, 王丰, 潘泉. 基于最大平均差异的迁移模糊C均值聚类[J]. 电子与信息学报. doi: 10.11999/JEIT220645
引用本文: 焦连猛, 王丰, 潘泉. 基于最大平均差异的迁移模糊C均值聚类[J]. 电子与信息学报. doi: 10.11999/JEIT220645
JIAO Lianmeng, WANG Feng, PAN Quan. Transfer Fuzzy C-Means Clustering Based on Maximum Mean Discrepancy[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT220645
Citation: JIAO Lianmeng, WANG Feng, PAN Quan. Transfer Fuzzy C-Means Clustering Based on Maximum Mean Discrepancy[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT220645

基于最大平均差异的迁移模糊C均值聚类

doi: 10.11999/JEIT220645
基金项目: 国家自然科学基金(62171386, 61801386, 61790552),陕西省重点研发计划(2022GY-081)
详细信息
    作者简介:

    焦连猛:男,博士,副教授,研究方向为机器学习、数据挖掘

    王丰:男,硕士生,研究方向为机器学习、数据挖掘

    潘泉:男,博士,教授,研究方向为信息融合、目标跟踪与识别

    通讯作者:

    焦连猛 jiaolianmeng@nwpu.edu.cn

  • 中图分类号: TN911.7; TP391.4

Transfer Fuzzy C-Means Clustering Based on Maximum Mean Discrepancy

Funds: The National Natural Science Foundation of China (62171386, 61801386, 61790552), Key Research and Development Program in Shaanxi Province (2022GY-081)
  • 摘要: 该文针对迁移聚类问题,提出一种基于最大平均差异的迁移模糊C均值(TFCM-MMD)聚类算法。TFCM-MMD解决了迁移模糊C均值聚类算法在源域与目标域数据分布差异大的情况下迁移学习效果减弱的问题。 该算法基于最大平均差异准则度量域间差异,通过学习源域和目标域的投影矩阵,以减小源域和目标域数据在公共子空间分布的差异,进而提升迁移学习的效果。最后,通过基于合成数据集和医学图像分割数据集的实验,进一步验证了TFCM-MMD算法在解决域间差异大的迁移聚类问题上的有效性。
  • 图  1  TFCM-MMD的算法思路

    图  2  在不同λ下TFCM和TFCM-MMD在T1_1上的聚类性能

    图  3  在不同λ下TFCM和TFCM-MMD在T1_2上的聚类性能

    图  4  实验用到的源域和目标域图像

    图  5  在不同λ下TFCM和TFCM-MMD在T2_1上的聚类性能

    图  6  在不同λ下TFCM和TFCM-MMD在T2_2上的聚类性能

    图  7  在不同λ下TFCM和TFCM-MMD在T2_3上的聚类性能

    图  8  聚类性能随m的变化趋势

    图  9  聚类性能随η的变化趋势

    图  10  聚类性能随$ \varepsilon $的变化趋势

    算法1 TFCM-MMD
     输入:源域数据${{\boldsymbol{X}}_{\text{s} } }$, 目标域数据${{\boldsymbol{X}}_{\text{t} } }$,源域聚类数$ {C_{\text{s}}} $, 目标域聚类数$ {C_{\text{t}}} $, 模糊加权系数$ {m_1} $, $ {m_2} $, 迁移率
        λ,学习率η, 最大迭代次数nmax, 终止阈值$ \varepsilon $
     输出:目标域模糊隶属度矩阵${\boldsymbol{U}}$
     (1) 根据源域聚类数$ {C_{\text{s}}} $, 利用FCM对源域数据${{\boldsymbol{X}}_{\text{s} } }$进行聚类, 获得源域的聚类中心${\tilde {\boldsymbol{V}}_k}$;
     (2) 根据目标域聚类数$ {C_{\text{t}}} $初始化模糊隶属度矩阵${\boldsymbol{U}}(0)$,聚类中心相关性矩阵${\boldsymbol{R}}(0)$,根据投影后矩阵的维数r初始化投影矩阵${\boldsymbol{H}}(0)$,迭代次
      数t=0;
     (3) 重复;
     (4) t=t+1;
     (5) 利用式(7)计算聚类中心${\boldsymbol{V}}(t)$;
     (6) 利用式(8)计算模糊隶属度矩阵${\boldsymbol{U}}(t)$;
     (7) 利用式(9)计算聚类中心相关性矩阵${\boldsymbol{R}}(t)$;
     (8) 利用式(15)计算投影矩阵${\boldsymbol{H}}(t)$;
     (9) 直到$ |{J_{{\text{TFCM - MMD}}}}(t) - {J_{{\text{TFCM - MMD}}}}(t - 1)| < \varepsilon $或者 t>nmax
    下载: 导出CSV

    表  1  不同噪声水平下TFCM与TFCM-MMD抗负迁移性能比较(以AC为例)(%)

    目标域数据TFCM最差聚类结果TFCM-MMD最差聚类结果聚类性能提升
    T2-169.8670.360.5
    T2-267.6471.674.0
    T2-361.2167.406.2
    下载: 导出CSV

    表  2  FCM-MMD与TFCM-MMD聚类性能对比(AC)

    S1_1-T1_1S1_2-T1_2S2-T2_1S2-T2_2S2-T2_3
    FCM-MMD0.6330.3300.7670.7000.624
    TFCM-MMD0.7670.7670.7470.7440.739
    CI*[0.6157, 0.9183][0.6157, 0.9183][0.7605, 0.7735][0.7373, 0.7507][0.7323, 0.7457]
    *最后一行是最佳方法的95%置信区间
    下载: 导出CSV

    表  3  FCM-MMD与TFCM-MMD聚类性能对比(RI)

    S1_1-T1_1S1_2-T1_2S2-T2_1S2-T2_2S2-T2_3
    FCM-MMD0.6390.3100.6940.6600.611
    TFCM-MMD0.7330.7360.6910.6880.684
    CI[0.5747, 0.8913][0.5783, 0.8937][0.6869, 0.7011][0.6809, 0.6951][0.6769, 0.6911]
    下载: 导出CSV

    表  4  FCM-MMD与TFCM-MMD聚类性能对比(DB)

    S1_1-T1_1S1_2-T1_2S2-T2_1S2-T2_2S2-T2_3
    FCM-MMD0.923\0.4730.5300.558
    TFCM-MMD0.7970.7970.5520.5500.556
    CI[0.6531, 0.9409][0.6531, 0.9409][0.4654, 0.4806][0.5224, 0.5376][0.5484, 0.5636]
    下载: 导出CSV
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  • 收稿日期:  2022-05-19
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